On 23 Sep 2013, at 12:41, Telmo Menezes wrote:
On Sat, Sep 21, 2013 at 9:43 PM, Bruno Marchal <[email protected]>
wrote:
On 21 Sep 2013, at 15:10, Telmo Menezes wrote:
On Fri, Sep 20, 2013 at 3:58 PM, Bruno Marchal <[email protected]>
wrote:
On 19 Sep 2013, at 16:51, Telmo Menezes wrote:
On Thu, Sep 19, 2013 at 4:31 PM, Bruno Marchal <[email protected]>
If so, can't we say ~D~t and thus []t?
Yes, []t is a theorem, of G and most modal logic, but not of Z!
Isn't the only situation where ~Dt the one where this is no world?
~Dt, that is [] f, inconsistency, is the type of the error, dream,
lie, and
"near-death", or in-a-cul-de-sac.
Thus your interest in near-death experiences?
Yes. And in all "extreme" altered state of consciousness. Those
extreme cases provide key information.
We should *try* to avoid it, but we can't avoid it without loosing
our
universality.
The consistent machines face the dilemma between security and lack of
freedom-universality. With <>p = ~[] ~p, here are equivalent way
to write
it:
<>t -> ~[]<>t
<>t -> <> [] f
[]<>t -> [] f
I don't understand how you arrive at this equivalence.
I use only the fact that (p -> q) is equivalent with (~q -> ~p) (the
contraposition rule, which is valid in classical propositional logic),
and the definition of <> p = ~[] ~p. I use also that ~~p is equivalent
with p.
Note that []p = ~~[]~~p = ~<> ~p. And,
~[]p = <> ~p
and
~<>p = [] ~p
Like with the quantifier, a not (~) jumping above a modal sign makes
it into a diamond, if it was a bo, and a box, if it was a diamond.
Starting from <>t -> ~[]<>t. Contraposition gives ~~[]<>t -> ~<>t, and
this gives by above, []<>t -> []~t, which gives
[]<>t -> []f (as ~t = f, and ~f = t).
OK?
For the third one, starting from the first one again: <>t -> ~[]<>t,
By contraposition []<>t -> ~<>t , but ~<>t = []~t = [] f.
OK?
Bruno
http://iridia.ulb.ac.be/~marchal/
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